Finite Group Databasebeta

← C131×#19472 #45705356

Subgroups — C131×#19472 #45705356

Order 33536.

592 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3210×C131C211yesmaximal, characteristic
2#3103×C131C211yesmaximal, characteristic
3#3078×C131C211yesmaximal, characteristic, complemented
4#2984×C131C211yesmaximal, characteristic, complemented
5#1704×C131C211yesmaximal, characteristic, complemented
6#1698×C131C211yesmaximal, characteristic, complemented
7#1690×C131C211yesmaximal, characteristic, complemented
8#1686×C131C211yesmaximal, characteristic, complemented
9#1684×C131C211yesmaximal, characteristic, complemented
10#1678×C131C211yesmaximal, characteristic, complemented
11#1670×C131C211yesmaximal, characteristic, complemented
12#1666×C131C211yesmaximal, characteristic, complemented
13#1574×C131C211yesmaximal, characteristic, complemented
14#1557×C131C211yesmaximal, characteristic
15#1554×C131C211yesmaximal, characteristic, complemented
16#533×C131C2211yescharacteristic
17#532×C131C2211yescharacteristic
18C2×C4×Q8×C131C2211yescharacteristic
19#494×C131C2211yescharacteristic
20#492×C131C2211yescharacteristic
21#487×C131C2211yescharacteristic
22#486×C131C2211yescharacteristic
23#481×C131—21no—
24#479×C131—21no—
25#479×C131—21no—
26#477×C131C2211yescharacteristic
27#477×C131C2211yescharacteristic
28#475×C131C2211yescharacteristic
29#475×C131C2211yescharacteristic
30#475×C131C2211yescharacteristic
31#475×C131C2211yescharacteristic
32#464×C131—21no—
33#464×C131—21no—
34#460×C131C2211yescharacteristic
35#460×C131C2211yescharacteristic
36#452×C131—21no—
37#452×C131—21no—
38#448×C131—21no—
39#446×C131—21no—
40#446×C131—21no—
41#446×C131C2211yescharacteristic
42#446×C131C2211yescharacteristic
43C8×Q8×C131C2211yescharacteristic
44C8×Q8×C131C2211yescharacteristic
45C4×SD16×C131—21no—
46C4×SD16×C131—21no—
47#432×C131—21no—
48#432×C131C2211yescharacteristic
49#431×C131—21no—
50#431×C131C2211yescharacteristic
51#431×C131C2211yescharacteristic
52#428×C131—21no—
53#423×C131C2211yescharacteristic
54#419×C131—21no—
55#335×C131C2211yescharacteristic
56#335×C131C2211yescharacteristic
57#334×C131C2211yescharacteristic
58#334×C131C2211yescharacteristic
59#333×C131C2211yescharacteristic
60#333×C131C2211yescharacteristic
61#332×C131C2211yescharacteristic
62#332×C131C2211yescharacteristic
63#332×C131C2211yescharacteristic
64#332×C131C2211yescharacteristic
65#331×C131C2211yescharacteristic
66#331×C131C2211yescharacteristic
67C2×#41×C131—21no—
68C22×Q8×C131D411yescharacteristic
69C2×Q16×C131—21no—
70C2×Q16×C131—21no—
71C2×SD16×C131—21no—
72C2×SD16×C131—21no—
73C2×SD16×C131—21no—
74C2×SD16×C131—21no—
75C2×M16×C131—21no—
76C4⋊Q8×C131C2311yescharacteristic
77C4⋊Q8×C131C2311yescharacteristic
78C4⋊Q8×C131C2311yescharacteristic
79#127×C131C2311yescharacteristic
80#125×C131—21no—
81#124×C131—21no—
82C22⋊Q8×C131—21no—
83C22⋊Q8×C131—21no—
84#121×C131—21no—
85#121×C131—21no—
86C4×Q8×C131—21no—
87C4×Q8×C131—21no—
88C4×Q8×C131—21no—
89C4×Q8×C131—21no—
90C4×Q8×C131D411yescharacteristic
91C4×Q8×C131D411yescharacteristic
92C4×Q8×C131C2311yescharacteristic
93C4×Q8×C131C2311yescharacteristic
94C4×D4×C131—21no—
95C4×D4×C131—21no—
96#117×C131—21no—
97C2×C4⋊C4×C131—21no—
98C2×C4⋊C4×C131D411yescharacteristic
99C2×C42×C131—21no—
100C2×C42×C131C2311yescharacteristic
101#107×C131—21no—
102#107×C131—21no—
103#106×C131—21no—
104#106×C131—21no—
105#106×C131—21no—
106#106×C131—21no—
107C4⋊C8×C131—21no—
108C4⋊C8×C131—21no—
109C4⋊C8×C131—21no—
110C4⋊C8×C131—21no—
111C4⋊C8×C131—21no—
112C4⋊C8×C131D411yescharacteristic
113C4⋊C8×C131D411yescharacteristic
114C4⋊C8×C131C2311yescharacteristic
115C4⋊C8×C131C2311yescharacteristic
116C4⋊C8×C131C2311yescharacteristic
117C4⋊C8×C131C2311yescharacteristic
118C4⋊C8×C131C2311yescharacteristic
119C4⋊C8×C131C2311yescharacteristic
120#103×C131—21no—
121#103×C131—21no—
122#103×C131—21no—
123#103×C131—21no—
124#103×C131—21no—
125#103×C131—21no—
126#103×C131—21no—
127#103×C131—21no—
128#102×C131—21no—
129#102×C131—21no—
130#102×C131—21no—
131#102×C131—21no—
132C22⋊C8×C131—21no—
133C22⋊C8×C131—21no—
134C22⋊C8×C131D411yescharacteristic
135C22⋊C8×C131D411yescharacteristic
136#97×C131—21no—
137#97×C131—21no—
138#97×C131—21no—
139C4×C8×C131—21no—
140C4×C8×C131—21no—
141C4×C8×C131—21no—
142C4×C8×C131C2311yescharacteristic
143C4×C8×C131C2311yescharacteristic
144#41×C131—81no—
145#41×C131—81no—
146C2×Q8×C131—21no—
147C2×Q8×C131—22no—
148C2×Q8×C131—21no—
149C2×Q8×C131—21no—
150C2×Q8×C131—21no—
151C2×Q8×C131—41no—
152C2×Q8×C131C2×D411yescharacteristic
153C2×Q8×C131C2×D411yescharacteristic
154C2×D4×C131—21no—
155C2×D4×C131—21no—
156C2×D4×C131—21no—
157C2×D4×C131—41no—
158C22×C4×C131—21no—
159C22×C4×C131—21no—
160C22×C4×C131—41no—
161C22×C4×C131C2×D411yescharacteristic
162C22×C4×C131C2×D411yescharacteristic
163C22×C4×C131#4111yescharacteristic
164Q16×C131—81no—
165Q16×C131—81no—
166SD16×C131—42no—
167SD16×C131—42no—
168SD16×C131—81no—
169SD16×C131—81no—
170M16×C131—42no—
171C2×C8×C131—21no—
172C2×C8×C131—21no—
173C2×C8×C131—21no—
174C2×C8×C131—21no—
175C2×C8×C131—21no—
176C2×C8×C131—21no—
177C2×C8×C131C2×D411yescharacteristic
178C2×C8×C131C2×D411yescharacteristic
179C2×C8×C131C2×D411yescharacteristic
180C2×C8×C131C2×D411yescharacteristic
181C4⋊C4×C131—21no—
182C4⋊C4×C131—21no—
183C4⋊C4×C131—21no—
184C4⋊C4×C131—21no—
185C4⋊C4×C131—21no—
186C4⋊C4×C131—21no—
187C4⋊C4×C131—21no—
188C4⋊C4×C131—21no—
189C4⋊C4×C131—21no—
190C4⋊C4×C131—21no—
191C4⋊C4×C131—21no—
192C4⋊C4×C131—41no—
193C4⋊C4×C131—41no—
194C4⋊C4×C131C2×D411yescharacteristic
195C4⋊C4×C131C2×D411yescharacteristic
196C22⋊C4×C131—41no—
197C22⋊C4×C131—41no—
198C22⋊C4×C131—41no—
199C42×C131—21no—
200C42×C131—21no—
201C42×C131—21no—
202C42×C131—21no—
203C42×C131—41no—
204C42×C131C2×D411yescharacteristic
205C42×C131C2×D411yescharacteristic
206C42×C131#4111yescharacteristic
207C42×C131C2411yescharacteristic
208C23×C131—41no—
209C23×C131#12111yescharacteristic
210Q8×C131—21no—
211Q8×C131—21no—
212Q8×C131—21no—
213Q8×C131—42no—
214Q8×C131—41no—
215Q8×C131—41no—
216Q8×C131—41no—
217Q8×C131—41no—
218Q8×C131—81no—
219Q8×C131#13712yes—
220D4×C131—41no—
221D4×C131—41no—
222D4×C131—41no—
223D4×C131—41no—
224D4×C131—81no—
225D4×C131—82no—
226C2×C4×C131—21no—
227C2×C4×C131—21no—
228C2×C4×C131—21no—
229C2×C4×C131—21no—
230C2×C4×C131—21no—
231C2×C4×C131—21no—
232C2×C4×C131—21no—
233C2×C4×C131—21no—
234C2×C4×C131—41no—
235C2×C4×C131—42no—
236C2×C4×C131—42no—
237C2×C4×C131—41no—
238C2×C4×C131—41no—
239C2×C4×C131—41no—
240C2×C4×C131—82no—
241C2×C4×C131#12111yescharacteristic
242C2×C4×C131#12111yescharacteristic
243C2×C4×C131#12111yescharacteristic
244C2×C4×C131C22×D411yescharacteristic
245C2×C4×C131C22×D411yescharacteristic
246C2×C4×C131C2×#4111yescharacteristic
247C8×C131—21no—
248C8×C131—21no—
249C8×C131—21no—
250C8×C131—21no—
251C8×C131—41no—
252C8×C131—41no—
253C8×C131—41no—
254C8×C131—41no—
255C8×C131—41no—
256C8×C131—41no—
257C22×C131—21no—
258C22×C131—21no—
259C22×C131—21no—
260C22×C131—81no—
261C22×C131—81no—
262C22×C131—81no—
263C22×C131C2×#12111yescharacteristic
264C4×C131—21no—
265C4×C131—21no—
266C4×C131—22no—
267C4×C131—21no—
268C4×C131—21no—
269C4×C131—41no—
270C4×C131—41no—
271C4×C131—41no—
272C4×C131—81no—
273C4×C131—81no—
274C4×C131—81no—
275C4×C131C2×#13711yescharacteristic
276C4×C131#57511yescharacteristic
277C4×C131#57711yescharacteristic
278C4×C131#57711yescharacteristic
279C2×C131—41no—
280C2×C131—161no—
281C2×C131#304311yescharacteristic
282C2×C131#305611yescharacteristic
283C2×C131#306711yescharacteristic
284#19472C13111yesmaximal, characteristic, direct product factor, Sylow
285C131#1947211yescharacteristic, direct product factor, Sylow
286#3210C2×C13111yescharacteristic
287#3103C2×C13111yescharacteristic
288#3078C2×C13111yescharacteristic, complemented
289#2984C2×C13111yescharacteristic, complemented
290#1704C2×C13111yescharacteristic, complemented
291#1698C2×C13111yescharacteristic, complemented
292#1690C2×C13111yescharacteristic, complemented
293#1686C2×C13111yescharacteristic, complemented
294#1684C2×C13111yescharacteristic, complemented
295#1678C2×C13111yescharacteristic, complemented
296#1670C2×C13111yescharacteristic, complemented
297#1666C2×C13111yescharacteristic, complemented
298#1574C2×C13111yescharacteristic, complemented
299#1557C2×C13111yescharacteristic
300#1554C2×C13111yescharacteristic, complemented
301#533C22×C13111yescharacteristic
302#532C22×C13111yescharacteristic
303C2×C4×Q8C22×C13111yescharacteristic
304#494C22×C13111yescharacteristic
305#492C22×C13111yescharacteristic
306#487C22×C13111yescharacteristic
307#486C22×C13111yescharacteristic
308#481—21no—
309#479—21no—
310#479—21no—
311#477C22×C13111yescharacteristic
312#477C22×C13111yescharacteristic
313#475C22×C13111yescharacteristic
314#475C22×C13111yescharacteristic
315#475C22×C13111yescharacteristic
316#475C22×C13111yescharacteristic
317#464—21no—
318#464—21no—
319#460C22×C13111yescharacteristic
320#460C22×C13111yescharacteristic
321#452—21no—
322#452—21no—
323#448—21no—
324#446—21no—
325#446—21no—
326#446C22×C13111yescharacteristic
327#446C22×C13111yescharacteristic
328C8×Q8C22×C13111yescharacteristic
329C8×Q8C22×C13111yescharacteristic
330C4×SD16—21no—
331C4×SD16—21no—
332#432—21no—
333#432C22×C13111yescharacteristic
334#431—21no—
335#431C22×C13111yescharacteristic
336#431C22×C13111yescharacteristic
337#428—21no—
338#423C22×C13111yescharacteristic
339#419—21no—
340#335C22×C13111yescharacteristic
341#335C22×C13111yescharacteristic
342#334C22×C13111yescharacteristic
343#334C22×C13111yescharacteristic
344#333C22×C13111yescharacteristic
345#333C22×C13111yescharacteristic
346#332C22×C13111yescharacteristic
347#332C22×C13111yescharacteristic
348#332C22×C13111yescharacteristic
349#332C22×C13111yescharacteristic
350#331C22×C13111yescharacteristic
351#331C22×C13111yescharacteristic
352C2×#41—21no—
353C22×Q8D4×C13111yescharacteristic
354C2×Q16—21no—
355C2×Q16—21no—
356C2×SD16—21no—
357C2×SD16—21no—
358C2×SD16—21no—
359C2×SD16—21no—
360C2×M16—21no—
361C4⋊Q8C23×C13111yescharacteristic
362C4⋊Q8C23×C13111yescharacteristic
363C4⋊Q8C23×C13111yescharacteristic
364#127C23×C13111yescharacteristic
365#125—21no—
366#124—21no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369#121—21no—
370#121—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8D4×C13111yescharacteristic
376C4×Q8D4×C13111yescharacteristic
377C4×Q8C23×C13111yescharacteristic
378C4×Q8C23×C13111yescharacteristic
379C4×D4—21no—
380C4×D4—21no—
381#117—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4D4×C13111yescharacteristic
384C2×C42—21no—
385C2×C42C23×C13111yescharacteristic
386#107—21no—
387#107—21no—
388#106—21no—
389#106—21no—
390#106—21no—
391#106—21no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8D4×C13111yescharacteristic
398C4⋊C8D4×C13111yescharacteristic
399C4⋊C8C23×C13111yescharacteristic
400C4⋊C8C23×C13111yescharacteristic
401C4⋊C8C23×C13111yescharacteristic
402C4⋊C8C23×C13111yescharacteristic
403C4⋊C8C23×C13111yescharacteristic
404C4⋊C8C23×C13111yescharacteristic
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417C22⋊C8—21no—
418C22⋊C8—21no—
419C22⋊C8D4×C13111yescharacteristic
420C22⋊C8D4×C13111yescharacteristic
421#97—21no—
422#97—21no—
423#97—21no—
424C4×C8—21no—
425C4×C8—21no—
426C4×C8—21no—
427C4×C8C23×C13111yescharacteristic
428C4×C8C23×C13111yescharacteristic
429#41—81no—
430#41—81no—
431C2×Q8—21no—
432C2×Q8—22no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—41no—
437C2×Q8C2×D4×C13111yescharacteristic
438C2×Q8C2×D4×C13111yescharacteristic
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—41no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—41no—
446C22×C4C2×D4×C13111yescharacteristic
447C22×C4C2×D4×C13111yescharacteristic
448C22×C4#41×C13111yescharacteristic
449Q16—81no—
450Q16—81no—
451SD16—42no—
452SD16—42no—
453SD16—81no—
454SD16—81no—
455M16—42no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8C2×D4×C13111yescharacteristic
463C2×C8C2×D4×C13111yescharacteristic
464C2×C8C2×D4×C13111yescharacteristic
465C2×C8C2×D4×C13111yescharacteristic
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4C2×D4×C13111yescharacteristic
480C4⋊C4C2×D4×C13111yescharacteristic
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—41no—
489C42C2×D4×C13111yescharacteristic
490C42C2×D4×C13111yescharacteristic
491C42#41×C13111yescharacteristic
492C42C24×C13111yescharacteristic
493C23—41no—
494C23#121×C13111yescharacteristic
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—42no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502Q8—41no—
503Q8—81no—
504Q8#137×C13112yes—
505D4—41no—
506D4—41no—
507D4—41no—
508D4—41no—
509D4—81no—
510D4—82no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—82no—
526C2×C4#121×C13111yescharacteristic
527C2×C4#121×C13111yescharacteristic
528C2×C4#121×C13111yescharacteristic
529C2×C4C22×D4×C13111yescharacteristic
530C2×C4C22×D4×C13111yescharacteristic
531C2×C4C2×#41×C13111yescharacteristic
532C8—21no—
533C8—21no—
534C8—21no—
535C8—21no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—41no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—81no—
546C22—81no—
547C22—81no—
548C22C2×#121×C13111yescharacteristic
549C4—21no—
550C4—21no—
551C4—22no—
552C4—21no—
553C4—21no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—81no—
558C4—81no—
559C4—81no—
560C4C2×#137×C13111yescharacteristic
561C4#575×C13111yescharacteristic
562C4#577×C13111yescharacteristic
563C4#577×C13111yescharacteristic
564C2—41no—
565C2—161no—
566C2#3043×C13111yescharacteristic
567C2#3056×C13111yescharacteristic
568C2#3067×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#121
commutator, Frattini, cosocleC42C24×C131
prime radical#532×C131C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #3078×C131C2semidirect
4. #2984×C131C2semidirect
5. #1704×C131C2semidirect
6. #1698×C131C2semidirect
7. #1690×C131C2semidirect
8. #1686×C131C2semidirect
9. #1684×C131C2semidirect
10. #1678×C131C2semidirect
11. #1670×C131C2semidirect
12. #1666×C131C2semidirect
13. #1574×C131C2semidirect
15. #1554×C131C2semidirect
284. #19472C131direct (N × H)
285. C131#19472direct (N × H)
288. #3078C2×C131semidirect
289. #2984C2×C131semidirect
290. #1704C2×C131semidirect
291. #1698C2×C131semidirect
292. #1690C2×C131semidirect
293. #1686C2×C131semidirect
294. #1684C2×C131semidirect
295. #1678C2×C131semidirect
296. #1670C2×C131semidirect
297. #1666C2×C131semidirect
298. #1574C2×C131semidirect
300. #1554C2×C131semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#3210×C1312
#3103×C1312
#3078×C1312
#2984×C1312
#1704×C1312
#1698×C1312
#1690×C1312
#1686×C1312
#1684×C1312
#1678×C1312
#1670×C1312
#1666×C1312
#1574×C1312
#1557×C1312
#1554×C1312
#19472131